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In the present paper, we are concerned with an SIS epidemicreaction-diffusion model governed by mass action infection mechanism and linearbirth-death growth with no flux boundary condition. By performing qualitativeanalysis, we study the stability of the disease-free equilibrium, uniformpersistence property in terms of the basic reproduction number and the globalstability of the endemic equilibrium in homogeneous environment, andinvestigate the asymptotic profile of endemic equilibria (when exist) inheterogeneous environment as one of the movement rate of the susceptible andinfected populations is small. Our results, together with those in previousworks on three other closely related modeling systems, suggest that the factorssuch as infection mechanism, variation of total population and populationmovement play vital but subtle roles in the transmission dynamics of diseasesand hence provide useful insights into the strategies designed for diseasecontrol and prevention.

On a diffusive SIS epidemic model with mass action mechanism and birth-death effect: Analysis, simulations and comparison with other mechanisms